The point process models to predict earthquake occurrences are roughly classified into two types except for the simplest Poisson process; one is the renewal process for earthquakes repeating periodically on the same hypocenter such as active faults and the other is the ETAS (Epidemic-type aftershock sequence) model taking the aftershock-triggering effect of every earthquake into account. However, relatively small repeating earthquakes have the characteristics of both models such that they usually recur periodically but their recurrence intervals get much shorter after nearby large earthquakes. In this paper, we propose a nonstationary renewal process model for such repeating earthquakes that incorporates the aftershock-triggering effect of nearby large earthquakes as a relative change in the loading rate. We apply the proposed model to the repeating earthquake catalog on Pacific Plate subduction zone in the northeastern Japan and evaluate probabilistic forecasts of the next repeating events considering the aftershock-triggering effect of the 2011 Tohoku earthquake.

Fault weakening due to slow slips of the fault or fluid intrusions by volcanic activities often induces earthquake swarm event. This type of seismicity has a different causal relationship to the seismic triggering sequence that precedes it in time, making it difficult to predict from the seismic catalog alone with the ETAS models commonly used to predict earthquakes. However, the use of geodesic data on crustal phenomena, which are the source of the triggering, will enable short-term prediction. The key point here is to show the correlation between geodetic data and a certain aspect of seismicity by using a statistical model. In this report, the transient correlation between swarm earthquakes and slow slip (or volcanic activity) was shown using a Bayesian based nonstationary ETAS model (Kumazawa and Ogata, 2013).

Uncovering the distribution of magnitudes and arrival times of aftershocks is a key to comprehending the characteristics of earthquake sequences, which enables us to predict seismic activities and conduct hazard assessments. However, identifying the number of aftershocks immediately after the main shock is practically difficult due to contaminations of arriving seismic waves. To overcome this difficulty, we construct a likelihood based on the detected data, incorporating a detection function to which Gaussian process regression (GPR) is applied. The GPR is capable of estimating not only the parameters of the distribution of aftershocks together with the detection function, but also credible intervals for both the parameters and the detection function. The property that the distributions of both the Gaussian process and aftershocks are exponential functions leads to an efficient Bayesian computational algorithm to estimate hyperparameters. After its validation through numerical tests, the proposed method is retrospectively applied to the catalog data related to the 2004 Chuetsu earthquake for the early forecasting of the aftershocks. The results show that the proposed method stably and simultaneously estimates distribution parameters and credible intervals, even within 3 hours after the main shock. 

The Earth’s continental crust is unique among the solar rocky planets and consists of various types of rocks, including igneous, metamorphic and sedimentary materials. The continental crust is broadly characterized by high concentrations of radiogenic elements such as U, Th and K, occupying ~40 % of these elements in the entire Earth’s system. In addition to the importance as the geochemical reservoir, the continental crust also plays a crucial role in geodynamic system, e.g., as a mechanical and thermal lid of the mantle convection system, which is related to the continental dispersal and coalesce. However, origin and growth mechanism of the continental crust have been largely controversial. To contribute to resolving this long-standing issue, precise estimates of the lithological and geochemical composition of the crust are essential. For this sake, we utilize and combine several different databases and methods that have been recently established: (1) the petrological and geochemical database of the Japan arc crustal rocks (DODAI, Haraguchi et al., 2018, http://dsap.jamstec.go.jp/DODAI/index.html), (2) the digitized geological map of the Japan arc (The Seamless Digital Geological Map of Japan (1:200,000), AIST, https://gbank.gsj.jp/seamless/), and (3) the multivariate statistical analyses that combines k-means cluster analysis and Independent Component Analysis (Iwamori et al., 2017, https://doi.org/10.1002/2016GC006663). As a first step, in this presentation, we report the quantitative method to estimate the average compositions of the exposed basement rocks and the individual lithologies, as well as their variability and statistical properties, mostly based on (1) and (2) above. These estimates will be useful to quantitatively discuss the origin and growth mechanism of the island arc system, once combined with the geochemical interpretation provided by the method (3) above.

We study the pattern formation via the time-dependent Ginzburg-Landau (TDGL) equation for the 2.5-dimensional kinetic Ising model. We include the dipole-dipole interaction and the effect from the material thickness by assuming the uniform structure along the normal direction to the surface of the material. We propose an effective equation based on the newly proposed categorization method of the phases of the two-dimensional spin system, which utilizes the spin Z₂ and spatial symmetries. The wavenumber representation of the TDGL equation reduces to the equilibrium equations by assuming a steady-state. However, the equilibrium equation is a set of cubic equations that have no analytic solutions in general. Thus, we further approximate the equilibrium equations using the restricted phase-space approximation proposed for the generic phi-4 models. The resultant effective equation is a set of quadratic equations. We confirmed the validity of the effective equation with the numerical time-evolution results by a home-made TDGL code for a system with up to 2¹⁸ spins. These effective equations show the simple underlying mechanism of the pattern formation that determines the phase to be realized in each set-up specified by a set of parameters (e.g., the interaction intensities and material thickness). This simple but powerful tool will enable us to analyze the phase-transitions in the Ising-like systems without solving the numerically massive TDGL equations directly.

Bayesian inversion constructs a posterior distribution of model parameters from observation equations and prior information, which are weighted by hyperparameters. In fully Bayesian inversion, we further suppose that the hyperparameters are also random variables and discuss the model- and hyper-parameters stochastically based on the joint posterior. However, it is unclear in the fully Bayesian inversion how we extract useful information about the model parameters, e.g., optimal values, from the joint posterior of the model- and hyper-parameters. 
In this study, we investigate the appropriate reduction of the joint posterior in the fully Bayesian inversion.  We classify the probability reduction into the following three cases by focusing on the marginalization of the posterior distribution: (1) non-marginalized joint posterior, (2) marginal posterior of the model parameters, and (3) marginal one of the hyperparameters. We first derived a suite of semi-analytic representations for the estimators of the maximum likelihood solution for each case in the linear inverse problems.  Then, we found that the solutions of the cases (1) and (2) are asymptotically the same when the number of the model parameters is large. Second, a synthetic test shows that appropriate reduction is realized by the case (3), known as in the Akaike Bayesian information criterion (ABIC). The cause of these results is that the joint posterior distribution concentrates delta-functionally on an under-fitted or over-fitted solution as the number of model parameters increases. This implies that the characteristic number of samples for the Monte Carlo methods explodes in computing the population average (EAP); namely, we have a problem of the sampling difficulty in the fully Bayesian inversion. 

Humpback whales (Megaptera novaeangliae) are an iconic cetacean species present in all major oceans. Nearly hunt to extinction, the species’ Southern Hemisphere populations have recovered in recent decades. Its annual migration between feeding and breeding grounds represents one of the largest animal migrations on earth, but also exposes them to a wide variety of environmental conditions. Limited research has been done to implement the effects of climate change into humpback whale life histories but is essential for estimating the future distribution and movements of this species. Here, a system-based research approach is presented, which uses coupled mechanistic models at appropriate length- and timescales that integrate, based on the importance of environmental drivers, key physical, biogeochemical, biological, and ecological system parameters. An extensive humpback whale database of sightings, in situ and remotely-sensed environmental data has been assembled and machine learning techniques are being employed to extract key behavioural responses to local environmental drivers. Outputs of these models consequently feed into behavioral agent-based models (ABMs) that simulate humpback whale movements through time and space under current and future climate scenarios. Preliminary results show that ABMs are able to reproduce migratory movements of E1 population humpback whales along the east coast of Australia and through the deep waters to Antarctica very well compared to validation data from sightings and satellite tracks. Given the high ecosystem and economic value of this species, we believe our approach advances international whaling conservation efforts and may be advanced to other marine species.

Although global circulation models (GCMs) have been used for the reconstruction of precipitation for selected geological time slices, there is a lack of a coherent set of precipitation models for the Mesozoic-Cenozoic period (the last 250 million years). There has been dramatic climate change during this time period capturing a super-continent hothouse climate, and continental breakup and dispersal associated with successive greenhouse and ice-house climate periods. We present an approach that links climate-sensitive sedimentary deposits such as coal, evaporites and glacial deposits to a global plate model, reconstructed paleo-elevation maps and high-resolution GCMs via Bayesian machine learning. We model the joint distribution of climate-sensitive sediments and annual precipitation through geological time, and use the dependency between sediments and precipitation to improve the models predictive accuracy.
Our approach provides a set of 13 data-driven global paleo-precipitation maps between 14 and 249 Ma, capturing major changes in long-term annual rainfall patterns as a function of plate tectonics, paleo-elevation and climate change at a low computational cost.